En este blog podrá leer los comentarios del autor y ver algunas fotografías de los lugares que visita y los trabajos que realiza. El objetivo: Dejar que los que esten interesados miren.
In this blog you will find comments of the author and some pictures of the places he visits and the jobs he is involved. The objective: Those who are interested can watch.

Translate

lunes, 9 de marzo de 2009

After a long time without posting - and thanks to a comment from Luciano - I am posting again.I read in a few blogs that posting periodically becomes an issue if we pursue long post. Some guys opt for reducing the length of their post in order to keep posting without big time gaps. I will try the same.Today I will reproduce a nice example taken from a discussion in a forum about physics ( alas in Spanish). The author of the post, Alejandro Kolton, was trying to introduce (and he did it!) the notion of sink and limit cycle in dynamical systems in a conceptual way. He proposed the following rule

TOE rule

Take an arbitrary Integer

Count the number of Odd digits, O=# Odd digits

Count the number of Even digits, E=# Even digits (including zeros)

Add the total, T=O+E

Write the number TOE

Go back to 2 and use this new number.

Applying the rule to any number will send you to a fixed value, namely321=TOErule(321)

A second rule was proposed by a forum member: Take into account the number ofzeros! The new rule is

TOEZ rule

Take an arbitrary Integer

Count the number of Odd digits, O=# Odd digits

Count the number of Even digits, E=# Even digits (excluding zeros)

Count the number of zeros, Z=# zeros

Add the total, T=O+E+Z

Write the number TOEZ

Go back to 2 and use this new number.

This new rule has a limit cycle of period 3.4211=TOEZrule(4031)4220=TOEZrule(4211)4031=TOEZrule(4220)